A novel approach for generalized Green-Naghdi-type electro-magneto-thermo-hyperelasticity wave propagation and reflection investigations in near-incompressible layers under shock loads

• Published in: Journal of thermal stresses Vol. 47; no. 6; pp. 743 - 765
• Main Authors: Mirparizi, M., Shariyat, M., Fotuhi, A. R.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.06.2024; Taylor & Francis Ltd
• Subjects: Algorithms; Elastic deformation; Electromagnetic fields; Free energy; Generalized electro-magneto-thermo-hyperelastic model; Iterative methods; Mathematical models; near-incompressible material; nonlinear Helmholtz free energy; nonlinear time-dependent finite element solution; Propagation; Shock loads; Sound propagation; Sound waves; Strain energy; Time dependence; Wave reflection
• ISSN: 0149-5739; 1521-074X
• DOI: 10.1080/01495739.2024.2338472

A novel nonlinear coupled finite-strain electro-magneto-thermo-hyperelasticity (EMTHE) model is developed for the first- and second-sound wave propagation and reflection investigations in media that are exposed to electromagnetic fields and mechanical shocks. In contrast to the previous studies which studied behaviors of the finite-strain elastic or incompressible materials with small deformations, the current research proposes a much more complicated but much more accurate novel practical model for wave propagation and reflection analyses in near-incompressible finite-strain materials. Furthermore, to evaluate the effects of the electro-magneto-thermomechanical coupling, the strain energy density function of the hyperelastic material is expanded in a new way. The governing equations are obtained according to a nonlinear version of the Helmholtz free energy. The energy equations comprise the first- and second-order time rates of the temperature to enable the modeling of the finite-speed heat transfer; i.e., the establishment of a second-sound model. A nonlinear iterative finite element solution algorithm is proposed and implemented for the resulting coupled time-dependent generalized electro-magneto-thermo-hyperelasticity equations. The results show significant differences between the predicted wave propagation and reflection characteristics and behaviors of the near-incompressible and incompressible finite-strain models.